James Glassman's Washington Post review of A Mathematician Plays the Stock Market
Published Sunday June 15, 2003 in Washington Post, Page F01
Trusting Markets to Be Efficient

Over the past few months, the stock market has put on one of those frequent demonstrations that show exactly why smart investors buy stocks and hold on to them -- or, better yet, why they consistently buy more.

The economic news has not been good, with unemployment rising to a nine-year high and the Federal Reserve warning of deflation. New corporate accounting scandals have surfaced. By conventional measures, stocks appear overvalued, with the price-to-earnings ratio for the benchmark Standard & Poor's 500-stock index exceeding 30. Yet stock prices keep rising. And rising.

Since March 11, the S&P is up by about one-fourth, the Nasdaq composite index by nearly 30 percent. The Russell 2000, an index of small-cap stocks, increased nine weeks in a row before falling last week, and the mega-cap stocks of the Dow Jones industrial average are up more than 9 percent this year.

Since May 19, the Dow has risen on 14 of 18 trading days. For the week that ended June 9, stocks that set new 12-month highs outnumbered stocks that set new lows by more than 100 to 1. Seventeen of the 20 stocks held by the greatest number of accounts have risen in 2003. And, of the 34 leading international stock indexes, 33 (all but those of Belgium, the Netherlands and India) show a gain for the year.

These numbers reinforce my market credo: "In the short term, no one knows anything."

That motto is also a crude way of expressing the Efficient Market Hypothesis -- or EMH, first formally presented in the 1964 dissertation of economist Eugene F. Fama but dating back more than a century, to the work of Louis Bachelier, a student of French mathematician Henri Poincare. Here is the way Fama put it:

"In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future."

In other words, millions of people, with vast incentives to learn every scrap of information about companies, are buying and selling billions of shares every day. Therefore, prices reflect the best knowledge of the present and predictions of the future. From today's perspective, tomorrow's prices are utterly unknowable.

As a result, prices tomorrow move in a phrase made popular by Princeton economist Burton G. Malkiel: a "random walk."

The problem with the EMH is that it denies our ability, as investors who think we are extremely cunning and perspicacious, to see the future. If you believe in the EMH, you understand that highly successful stock selections are really just lucky guesses. More important, all of that forecasting you hear on CNBC and read in the newspapers and magazines is just blather -- as is "technical analysis," the interpretation of lines on charts that show "resistance levels" and "head and shoulders" formations.

A recent piece of spam in my e-mail box from Zacks.com offers "Market Timing Secrets From the Man Who Called the Current Bull Run." Ridiculous. Ian McDonald writes in the Wall Street Journal, "History says this type of run-up doesn't usually keep its head of steam." That's like solemnly predicting that the next flip of a coin will be heads.

But, to tell the truth, while I believe in the EMH intellectually, I have a hard time acting on it.

According to John Allen Paulos, author of a wonderful new book, "A Mathematician Plays the Stock Market" (Basic Books), that's all to the good. The paradox, he told me in an interview last week, is that, if all investors were convinced that markets were efficient, they would simply sit on their holdings, never buying or selling. In such a world, new information about stocks would never enter the market, moving the prices of stocks in an efficient way.

"The EMH is true," he said, "to the extent that people believe it to be false and so, by their exertions, bring about efficiency." Cool.

This is what Paulos does best -- identify paradoxes and puzzles, not just in the market but also in everyday life. He is the author of one of my favorite books of all time, "Innumeracy," published in 1988. The book's title is a term he invented to describe the mathematical illiteracy of Americans -- exploited daily by such institutions as state-run lotteries, which Voltaire, more than 200 years ago, called a "tax on stupidity."

Paulos is a professor of mathematics at Temple University, a columnist for ABCNews.com and a great storyteller. He begins his new book by citing the insight of economist John Maynard Keynes that stock picking is akin to a beauty contest, where the object is not to choose the prettiest woman but to choose the woman who others think is the prettiest. Investors must anticipate, Keynes wrote, "what average opinion expects the average opinion to be." (This is the theme of many TV quiz shows, including "Family Feud.") But Paulos points out that guessing average opinion is not so easy. He writes:

"Consider a situation in which the individuals in a group must simultaneously choose a number between 0 and 100. They are further directed to pick the number they think will be close to 80 percent of the average number chosen by the group." The winner gets $100. Which number would you pick? Well, you might reason that the average number is 50; therefore, the number to pick would be 40, which is 80 percent of 50.

But, says Paulos, "others might anticipate that people will guess 40 for this reason and so they would guess 32, which is 80 percent of 40. Still others might anticipate that people will guess 32 for this reason and so they would guess 25.6, which is 80 percent of 32."

This kind of thinking progresses until the players reach "the optimal response, which is 0" -- that is, the Nash Equilibrium of the game (Nash being John Nash, the Nobel mathematician who was the subject of the book and movie "A Beautiful Mind").

"The problem of guessing 80 percent of the average guess," writes Paulos, is like "Keynes's description of the investors' task. What makes it tricky is that anyone bright enough to cut to the heart of the problem and guess 0 right away is almost certain to be wrong since different individuals will engage in different degrees of meta-reasoning about others' reasoning."

Keynes, by all accounts, was a successful investor, but I wouldn't suggest you follow his approach. Consider a contemporary example: mortgage maker Freddie Mac (FRE), whose stock dropped 15 percent in a single day last week on news that top executives were booted out in an accounting investigation. If you believe that investing is a beauty contest, what's your move? Will investors now start bidding up the price of Freddie, sensing that others will see that its decline has made it cheap? Or do they predict that the decline in the stock price will scare other investors off, driving the price ever lower?

There is really no answer -- either at the level of individual stocks or the market as a whole. And trying to divine the psychological reactions of other investors is excruciatingly difficult. Yes, Princeton economist Daniel Kahneman last year won the Nobel Prize in economics for his work with the late Amos Tversky on behavioral foibles (for example, that investors tend to assume less risk to obtain gains than they do to avoid losses). But even Richard H. Thaler, one of the leading behavioral economists, warns investors not to try to profit from behavioral analysis.

"While behaviorists think that it is theoretically possible to beat the market," Thaler was quoted as saying last week by Dirk Olin in the New York Times, "individual investors do not have the time or training to do that on their own, and finding superior skills among active mutual fund managers is not easy, either."

It's a better strategy simply to trust in the EMH. Even if the hypothesis isn't perfect, Malkiel says, "you ought to act as if the markets are efficient."

In an efficient market, we can't tell the future simply by looking at the past. "If the market has done well (or poorly) over a given time period in the past," writes Paulos, "there is no strong tendency for it to do well (or poorly) during the next time period."

Such an admission of ignorance is the beginning of wisdom. If we can't know the future, we can stop spending time on trying to pick the precisely correct stocks at the precisely correct times. We can forget about market timing and simply take advantage of the market's broad tendency to rise.

Like a coin that's slightly biased toward heads, the market will, over time, go up more than down. The average returns to U.S. stocks -- both price increases and dividends -- over long periods are remarkably consistent: about 10 percent annually, or roughly 7 percent after inflation. And for good reasons: first, the companies that issue shares increase their profits at roughly the rate of economic growth, or about 6 percent (including inflation) annually, and, second, the market pays investors for taking risks. How to benefit from the EMH and the bias?

By investing in portfolios that are broadly diversified and carry low expenses -- for example, index mutual funds such as Vanguard 500 Index (VFINX), which tracks the S&P, charges less than 0.2 percent in fees (compared with an average 1.4 percent for other stock funds) and also happens to be the largest fund in the world. Even Thaler agrees that you should "settle for the average returns and low fees offered by index funds."

"People need a conceptual map of the market," Paulos told me last week. The EMH provides it. But, he adds, it is important not to become dogmatic. As super-investor Warren Buffett once told his shareholders, "observing that the market was frequently efficient, [the EMH enthusiasts] went on to conclude incorrectly that the market was always efficient. The difference between the propositions is night and day."

Paulos agrees with Buffett's demurral, and so do I. The EMH can get carried to extremes. Paulos cites the old joke about the two efficient-market theorists walking down the street: "They spot a hundred-dollar bill on the sidewalk and pass it by, reasoning that if it were real, it would have been picked up already."

So let's be clear: There are inefficiencies in the market. Investors do get carried away. Mister Market, the metaphor invented by Buffett's mentor, Benjamin Graham, is truly a manic-depressive, who swings from extreme pessimism to extreme optimism.

Buying shares of a company because you think they are cheap is not an irrational act. Investing in mutual funds run by managers who aspire to beat the market is not insane. But the EMH must be the default position, the pole, the home base of your investing life. When you think you can "beat" the market, you need to examine your assumptions and your hubris.

A personal example: In December, I bought shares of Home Depot (HD) at $24.75 because I thought the company had become absurdly undervalued. Ten days later, I bought more at $21.50. On Friday it was trading at $33.56. I thought I was smart. But was I just lucky? I will never know. But it is probably better for me to think it was luck so that I don't rashly conclude that I can discover cheap stocks with consistency. I can't. Neither can you. Neither can anyone.

Still, the quest to beat the market is gloriously human. Don't deny it. Just put it in the proper perspective.

One possible inefficiency that has always interested me involves cash flow. By definition, the value of a stock is determined by the flow of free cash it generates for investors -- not by the earnings numbers it renders quarterly through the arcane rules of generally accepted accounting principles. Often, of course, GAAP earnings and cash flow are the same, but not always.

In its new issue, Dow Theory Forecasts points to several stocks that have displayed consistently strong increases over the past five years in their "cash from operations" (part of the statement of cash flows that every company files). Among them: Anheuser-Busch (BUD), brewing; Merck (MRK), drugs; Pentair (PNR), tools and fluid products; Colgate-Palmolive (CL), consumer products; Harley-Davidson (HDI), motorcycles; and Wal-Mart Stores (WMT), the world's largest retailer.

Notice that in a column that extols the virtues of the EMH, I have managed to drop some crowd-pleasing stock tips. Toward the end of our interview, I asked the wry and paradox-prone Professor Paulos about his own picks. "Oh," he said, "they're on Page 282 of the book."

The book ends on Page 216.

Of the stocks mentioned in this article, James K. Glassman owns Home Depot. His e-mail address is jglassman@aei.org. John Allen Paulos's Web site is www.math.temple.edu/paulos.

2003 The Washington Post Company